Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2506.05865

Strong Mitigation of the Magnetic-Field-Induced Frequency Shift in Coherent-Population-Trapping Atomic Clocks

Denis V. Brazhnikov, V. I. Vishnyakov, Mikhail N Skvortsov

Published Jun 6, 2025• 0 citations
arXivHTMLPDF

Abstract

We study the magnetic-field-induced frequency shift (MFS) of the clock (``0--0'') transition in coherent-population-trapping (CPT) microwave atomic clock. It is shown that the use of the Pound-Drever-Hall-like (PDH) technique for frequency locking provides brilliant opportunities for mitigating the MFS. Using a $0.125$ cm$^3$ rubidium vapor cell with a buffer gas, we have measured a residual sensitivity of the clock transition frequency to be $\approx\,72$ $μ$Hz/mG over $\approx\,$$6$ mG interval. It means that a fractional frequency shift is extremely small ($\approx\,$$1$$\,\times\,$$10^{-14}$ mG$^{-1}$). The results contribute to the development of a new-generation CPT-based miniature atomic clock (MAC) with improved long-term frequency stability. The proposed method is quite general and can be used for other excitation schemes in atomic clocks, including Ramsey-like techniques.

DOI
10.48550/arxiv.2506.05865

Related papers

Mitigation of the magnetic-field-induced frequency shift in coherent-population-trapping atomic clocks

Denis V. Brazhnikov, V. I. Vishnyakov, Mikhail N Skvortsov

We study the magnetic-field-induced frequency shift (MFS) of the reference resonance in a coherent population trapping (CPT) microwave atomic clock. It is shown that the use of the Pound–Drever–Hall-like technique for frequency locking provides brilliant opportunities for mitigating the MFS. Using a 0.125 cm3 rubidium vapor cell with a buffer gas, we have measured a residual sensitivity of the reference CPT resonance frequency to be ≈70μHz/mG over ≈6 mG interval. It means that a fractional frequency shift is extremely small (≈1×10−14 mG−1). The results contribute to the development of a new-generation CPT-based miniature atomic clock with improved long-term frequency stability. The proposed method is sufficiently versatile and can be adapted for other excitation schemes in atomic clocks, including those based on Ramsey-like or double-resonance techniques.

Applied Physics Letters•Dec 29, 2025•1 citation

Reduction of magnetic-field-induced shift in quantum frequency standards based on coherent population trapping

V. I. Vishnyakov, Denis V. Brazhnikov, Mikhail N Skvortsov

We investigate the magnetic-field-induced frequency shift (MFS) of the clock “0–0” transition in the microwave quantum frequency standard (atomic clock) based on coherent population trapping (CPT) in 87Rb vapor. To scan the CPT resonance and to form the error signal, a method analogous to the Pound–Drever–Hall (PDH) technique in the optical frequency range is employed, where the modulating frequency (fm) significantly exceeds the resonance linewidth (FWHM). The experiments demonstrate that this technique offers brilliant capabilities for controlling the sensitivity of the clock transition frequency to magnetic field variations in the vapor cell compared to the conventional method with low-frequency modulation (fm≪FWHM). Specifically, the PDH technique provides several optimal values of the bias magnetic field generated by the solenoid, at which the “0–0” transition frequency exhibits extremely low sensitivity to small variations in the external magnetic field. Furthermore, these magnetic field values can be easily adjusted by changing fm, which is relevant for the optimization of the atomic clock’s operating regime. The experimental results show that by using the PDH technique, the influence of MFS on the clock transition can be suppressed down to ≈3.2×10−13δB2mG−2. These findings can be leveraged both to relax stringent requirements for magnetic field shielding in state-of-the-art CPT-based miniature atomic clocks and to build a new generation of such clocks with long-term frequency stability better than 10−12.

arXiv:2502.11587•Journal of Applied Physics•Apr 25, 2025•6 citations

Light shift mitigation in microcell-based coherent-population-trapping atomic clocks in the field of two circularly polarized light beams

Denis V. Brazhnikov, S M Ignatovich, Mikhail N Skvortsov

State-of-the-art miniature atomic clocks (MACs) are based on the phenomenon of coherent population trapping (CPT) in alkali-metal atomic vapors ($\mathrm{Rb}$ or $\mathrm{Cs}$). Improving the stability of the clock frequency is a crucial issue; resolving it would result in significant progress in numerous applications. Here, we examine the configuration of the light field, which is composed of two bichromatic beams with opposing handedness of circular polarization. The beams are in resonance with optical transitions in the $\mathrm{Cs}$ ${D}_{1}$ line ($\ensuremath{\lambda}\ensuremath{\approx}895$ nm). This configuration has previously been shown to produce observed CPT resonances with higher contrast than a standard single-beam scheme; however, our scheme implements pump and probe beams that operate independently, with the transmission of the probe beam being monitored separately. This approach differs from previous studies. The experiments are carried out using a cubic $5\ifmmode\times\else\texttimes\fi{}5\ifmmode\times\else\texttimes\fi{}5\phantom{\rule{0.2em}{0ex}}{\mathrm{mm}}^{3}$ vapor cell filled with buffer gas. It is shown that the line shape of the resonance acquires an asymmetry that can be efficiently controlled by a microwave (Raman) phase between the beams. As a proof of concept, we study the way in which this asymmetry can help to mitigate the influence of the ac Stark (light) shift on the long-term frequency stability of CPT clocks based on vapor microcells ($V\ensuremath{\ll}1\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{3}$). Experimental verification is performed with both a distributed-Bragg-reflector laser and a vertical-cavity surface-emitting laser. The latter is of particular importance for the development of MACs. The experimental results are in qualitative agreement with the analytical theory based on a double-$\mathrm{\ensuremath{\Lambda}}$ scheme of atomic energy levels.

arXiv:2311.00461•Physical Review Applied•May 23, 2024•8 citations

Frequency Shifts in a Coherent Population Trapping Cs Vapor Cell Atomic Clock

Juliette Breurec, Moustafa Abdel Hafiz, Claudio Eligio Calosso +2 more

We report on measurements of frequency shifts in a microwave cesium vapor cell atomic clock based on coherent population trapping (CPT). The dependence of the clock frequency on numerous experimental parameters, such as the laser power, the laser frequency, the microwave power, the cell temperature, the static magnetic field, but also the temperature of some key components, or the translation and rotation of critical wave plates and optical elements, is investigated. The stability budget of the clock frequency at one day is reported and discussed. This study constitutes a solid database for the future demonstration of a CPT-based cell clock with enhanced mid- and long-term stability performances.

IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control•May 29, 2025•4 citations

A coherent population trapping Cs vapor cell atomic clock based on push-pull optical pumping

Moustafa Abdel Hafiz, Rodolphe Boudot

This article reports on the characterization of a compact coherent-population-trapping (CPT) Cs vapor cell atomic clock using the push-pull optical pumping technique. This method allows to detect high-contrast CPT resonances on the 0-0 magnetic-field insensitive clock transition. The clock short-term fractional frequency stability is measured to be 3×10−13 τ−1/2 up to 100 s averaging time, in correct agreement with the signal-to-noise ratio limit. These results are among the best performances ever reported for a CPT-based clock. The noise budget is detailed. A preliminary study is reported to evaluate limitations to the clock mid-term frequency stability. The clock performances are found to be presently mainly limited in the mid-term by laser power effects.

Journal of Applied Physics•Sep 28, 2015•49 citations

Limitations of Long-Term Stability in a Coherent Population Trapping Cs Clock

Olga Kozlova, Jean-Marie Danet, Stéphane Guérandel +1 more

Vapor cell atomic clocks exhibit reduced frequency stability for averaging time between about one hundred and a few thousand seconds. Here we report a study on the impact of the main parameters on the mid-to-long term instability of a buffer-gas vapor cell Cs clock, based on coherent population trapping (CPT). The CPT signal is observed on the Cs D1 line transmission, using a double Λ scheme and a Ramsey interrogation technique. The effects on the clock frequency of the magnetic field, the cell temperature, and the laser intensities are reported. We show in particular that the laser intensity shift is temperature dependent. Along with the laser intensity ratio and laser polarization properties, this is one of the most important parameters.

arXiv:1311.1991•IEEE Transactions on Instrumentation and Measurement•Jan 31, 2014•59 citations
We study the magnetic-field-induced frequency shift (MFS) of the clock (``0--0'') transition in coherent-population-trapping (CPT) microwave atomic clock. It is shown that the use of the Pound-Drever-Hall-like (PDH) technique for frequency locking provides brilliant opportunities for mitigating the MFS. Using a 0.1250.1250.125 cm3^33 rubidium vapor cell with a buffer gas, we have measured a residual sensitivity of the clock transition frequency to be ≈ 72\approx\,72≈72 μμμHz/mG over \approx\,$$6 mG interval. It means that a fractional frequency shift is extremely small (\approx\,$$1$$\,\times\,$$10^{-14} mG−1^{-1}−1). The results contribute to the development of a new-generation CPT-based miniature atomic clock (MAC) with improved long-term frequency stability. The proposed method is quite general and can be used for other excitation schemes in atomic clocks, including Ramsey-like techniques.
We study the magnetic-field-induced frequency shift (MFS) of the reference resonance in a coherent population trapping (CPT) microwave atomic clock. It is shown that the use of the Pound–Drever–Hall-like technique for frequency locking provides brilliant opportunities for mitigating the MFS. Using a 0.125 cm3 rubidium vapor cell with a buffer gas, we have measured a residual sensitivity of the reference CPT resonance frequency to be ≈70μHz/mG over ≈6 mG interval. It means that a fractional frequency shift is extremely small (≈1×10−14 mG−1). The results contribute to the development of a new-generation CPT-based miniature atomic clock with improved long-term frequency stability. The proposed method is sufficiently versatile and can be adapted for other excitation schemes in atomic clocks, including those based on Ramsey-like or double-resonance techniques.
We investigate the magnetic-field-induced frequency shift (MFS) of the clock “0–0” transition in the microwave quantum frequency standard (atomic clock) based on coherent population trapping (CPT) in 87Rb vapor. To scan the CPT resonance and to form the error signal, a method analogous to the Pound–Drever–Hall (PDH) technique in the optical frequency range is employed, where the modulating frequency (fm) significantly exceeds the resonance linewidth (FWHM). The experiments demonstrate that this technique offers brilliant capabilities for controlling the sensitivity of the clock transition frequency to magnetic field variations in the vapor cell compared to the conventional method with low-frequency modulation (fm≪FWHM). Specifically, the PDH technique provides several optimal values of the bias magnetic field generated by the solenoid, at which the “0–0” transition frequency exhibits extremely low sensitivity to small variations in the external magnetic field. Furthermore, these magnetic field values can be easily adjusted by changing fm, which is relevant for the optimization of the atomic clock’s operating regime. The experimental results show that by using the PDH technique, the influence of MFS on the clock transition can be suppressed down to ≈3.2×10−13δB2mG−2. These findings can be leveraged both to relax stringent requirements for magnetic field shielding in state-of-the-art CPT-based miniature atomic clocks and to build a new generation of such clocks with long-term frequency stability better than 10−12.
State-of-the-art miniature atomic clocks (MACs) are based on the phenomenon of coherent population trapping (CPT) in alkali-metal atomic vapors (Rb\mathrm{Rb}Rb or Cs\mathrm{Cs}Cs). Improving the stability of the clock frequency is a crucial issue; resolving it would result in significant progress in numerous applications. Here, we examine the configuration of the light field, which is composed of two bichromatic beams with opposing handedness of circular polarization. The beams are in resonance with optical transitions in the Cs\mathrm{Cs}Cs D1{D}_{1}D1​ line ($\ensuremath{\lambda}\ensuremath{\approx}895$ nm). This configuration has previously been shown to produce observed CPT resonances with higher contrast than a standard single-beam scheme; however, our scheme implements pump and probe beams that operate independently, with the transmission of the probe beam being monitored separately. This approach differs from previous studies. The experiments are carried out using a cubic $5\ifmmode\times\else\texttimes\fi{}5\ifmmode\times\else\texttimes\fi{}5\phantom{\rule{0.2em}{0ex}}{\mathrm{mm}}^{3}$ vapor cell filled with buffer gas. It is shown that the line shape of the resonance acquires an asymmetry that can be efficiently controlled by a microwave (Raman) phase between the beams. As a proof of concept, we study the way in which this asymmetry can help to mitigate the influence of the ac Stark (light) shift on the long-term frequency stability of CPT clocks based on vapor microcells ($V\ensuremath{\ll}1\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{3}$). Experimental verification is performed with both a distributed-Bragg-reflector laser and a vertical-cavity surface-emitting laser. The latter is of particular importance for the development of MACs. The experimental results are in qualitative agreement with the analytical theory based on a double-$\mathrm{\ensuremath{\Lambda}}$ scheme of atomic energy levels.
We report on measurements of frequency shifts in a microwave cesium vapor cell atomic clock based on coherent population trapping (CPT). The dependence of the clock frequency on numerous experimental parameters, such as the laser power, the laser frequency, the microwave power, the cell temperature, the static magnetic field, but also the temperature of some key components, or the translation and rotation of critical wave plates and optical elements, is investigated. The stability budget of the clock frequency at one day is reported and discussed. This study constitutes a solid database for the future demonstration of a CPT-based cell clock with enhanced mid- and long-term stability performances.
This article reports on the characterization of a compact coherent-population-trapping (CPT) Cs vapor cell atomic clock using the push-pull optical pumping technique. This method allows to detect high-contrast CPT resonances on the 0-0 magnetic-field insensitive clock transition. The clock short-term fractional frequency stability is measured to be 3×10−13 τ−1/2 up to 100 s averaging time, in correct agreement with the signal-to-noise ratio limit. These results are among the best performances ever reported for a CPT-based clock. The noise budget is detailed. A preliminary study is reported to evaluate limitations to the clock mid-term frequency stability. The clock performances are found to be presently mainly limited in the mid-term by laser power effects.
Vapor cell atomic clocks exhibit reduced frequency stability for averaging time between about one hundred and a few thousand seconds. Here we report a study on the impact of the main parameters on the mid-to-long term instability of a buffer-gas vapor cell Cs clock, based on coherent population trapping (CPT). The CPT signal is observed on the Cs D1 line transmission, using a double Λ scheme and a Ramsey interrogation technique. The effects on the clock frequency of the magnetic field, the cell temperature, and the laser intensities are reported. We show in particular that the laser intensity shift is temperature dependent. Along with the laser intensity ratio and laser polarization properties, this is one of the most important parameters.